This paper studies the question to what extent premia for macroeconomic risks in banking are sufficient to avoid banking crises. We investigate a competitive banking system embedded in an overlapping generation model subject to repeated macroeconomic shocks. We show that even if banks fully incorporate macroeconomic risks in their pricing of loans, a banking system may enter bankruptcy with a probability of one. A major cause for this default is that risk premia of a competitive banking system may become too small if the capital base is low.